Extracts meta-features from datasets to support the design of recommendation systems based on Meta-Learning (MtL). The meta-features, also called characterization measures, are able to characterize the complexity of datasets and to provide estimates of algorithm performance. The package contains not only the standard, but also more recent characterization measures. By making available a large set of meta-feature extraction functions, this package allows a comprehensive data characterization, a deep data exploration and a large number of MtL-based data analysis.

In MtL, meta-features are designed to extract general properties able to characterize datasets. The meta-feature values should provide relevant evidences about the performance of algorithms, allowing the design of MtL-based recommendation systems. Thus, these measures must be able to predict, with a low computational cost, the performance of the algorithms under evaluation. In this package, the meta-feature measures are divided into five groups:

**General**: General information related to the dataset, also known as simple measures, such as number of instances, attributes and classes.**Statistical**: Standard statistical measures to describe the numerical properties of a distribution of data and also the discriminant measures.**Information-theoretic**: Particularly appropriate to describe discrete (categorical) attributes and their relationship with the classes.**Decision Tree Model-based**: Measures designed to extract characteristics like the depth, the shape and size of a Decision Tree (DT) model induced from a dataset.**Landmarking**: Represents the performance of simple and efficient learning algorithms.

In the following sections we will briefly introduce how to use the `mfe`

package to extract all the measures using standard methods as well as to extract specific measures using methods for each group. Once the package is loaded, the vignette is also available inside R with the command `browseVignettes`

.

The standard way to extract meta-features is using the `metafeatures`

methods. The method can be used by a symbolic description of the model (formula) or by a data frame. The parameters are the dataset and the group of measures to be extracted. By default, the method extract all the measures. For instance:

```
library(mfe)
## Extract all measures using formula
iris.info <- metafeatures(Species ~ ., iris)
## Extract all measures using data frame
iris.info <- metafeatures(iris[,1:4], iris[,5])
## Extract general, statistical and information-theoretic measures
iris.info <- metafeatures(Species ~ ., iris,
groups=c("general", "statistical", "infotheo"))
```

Several measures return more than one value. To aggregate them, post processing methods can be used. It is possible to compute min, max, mean, median, kurtosis, standard deviation, among others. The default methods are the `mean`

and the `sd`

. For instance:

To customize the measure extraction, is necessary to use specific methods for each group of measures. For instance, `infotheo`

and `statistical`

compute the information theoretical and the statistical measures, respectively. The following examples illustrate these cases:

```
## Extract two information theoretical measures
stat.iris <- infotheo(Species ~ ., iris,
features=c("attrEnt", "jointEnt"))
## Extract three statistical measures
disc.iris <- statistical(Species ~ ., iris,
features=c("cancor", "cor", "iqr"))
## Extract the histogram for the correlation measure
hist.iris <- statistical(Species ~ ., iris,
features="cor", summary="hist")
```

Different from the `metafeatures`

method, these methods receive a parameter called `features`

, to define which features are required, and return a list instead of a numeric vector. In additional, some groups can be customized using additional arguments.

There are five measure groups which can be either general information about the dataset, statistical information, descriptors about information theoretical, measures designed to extract characteristics about the DT model or landmarks which represent the performance of simple algorithms applied to the dataset. The following example show the available groups:

```
## [1] "general" "statistical" "infotheo" "model.based" "landmarking"
## [6] "relative" "clustering"
```

These are the most simple measures for extracting general properties of the datasets. For instance, `nrAttr`

and `nrClass`

are the total number of attributes in the dataset and the number of output values (classes) in the dataset, respectively. To list the measures of this group use `ls.general()`

. The following examples illustrate these measures:

```
## [1] "attrToInst" "catToNum" "freqClass" "instToAttr" "nrAttr"
## [6] "nrBin" "nrCat" "nrClass" "nrInst" "nrNum"
## [11] "numToCat"
```

```
## Extract all general measures
general.iris <- general(Species ~ ., iris)
## Extract two general measures
general(Species ~ ., iris, features=c("nrAttr", "nrClass"))
```

```
## $nrAttr
## [1] 4
##
## $nrClass
## [1] 3
```

The general measures return a list named by the requested measures. The `post.processing`

methods are applied only for the `freqClass`

meta-feature. For instance, to extract the minimum, maximum and the standard deviation of the classes proportion use:

```
## Extract two general measures
general(Species ~ ., iris, features="freqClass", summary=c("min", "max", "sd"))
```

```
## $freqClass
## min max sd
## 0.3333333 0.3333333 0.0000000
```

Statistical meta-features are the standard statistical measures to describe the numerical properties of a distribution of data. As it requires only numerical attributes, the categorical data are transformed to numerical. For instance, `cor`

and `skewness`

are the absolute correlation between of each pair of attributes and the skewness of the numeric attributes in the dataset, respectively. To list the measures of this group use `ls.statistical()`

. The following examples illustrate these measures:

```
## [1] "canCor" "gravity" "cor" "cov" "nrDisc"
## [6] "eigenvalues" "gMean" "hMean" "iqRange" "kurtosis"
## [11] "mad" "max" "mean" "median" "min"
## [16] "nrCorAttr" "nrNorm" "nrOutliers" "range" "sd"
## [21] "sdRatio" "skewness" "sparsity" "tMean" "var"
## [26] "wLambda"
```

```
## Extract all statistical measures
stat.iris <- statistical(Species ~ ., iris)
## Extract two statistical measures
statistical(Species ~ ., iris, features=c("cor", "skewness"))
```

```
## $cor
## mean sd
## 0.5941160 0.3375443
##
## $skewness
## mean sd
## 0.06273198 0.29439896
```

The statistical group can use two additional parameter called `by.class`

and `transform`

. To the former the default is `by.class=FALSE`

which means that the meta-features are computed without consider the classes values. Otherwise, the measure is extracted using the instances separated by class. In the latter, the default value is `transform=TRUE`

which means that categorical attributes will be transformed to numeric. The following example shows the use of these two definitions:

```
## Extract correlation using instances by classes
statistical(Species ~ ., iris, features="cor", by.class=TRUE)
```

```
## $cor
## mean sd
## 0.4850530 0.2124471
```

```
## Ignore the class attributes
aux <- cbind(class=iris$Species, iris)
statistical(Species ~ ., aux, transform=FALSE)
```

```
## $canCor
## mean sd
## 0.7280090 0.3631869
##
## $gravity
## [1] 3.208281
##
## $cor
## mean sd
## 0.5941160 0.3375443
##
## $cov
## mean sd
## 0.5966542 0.5582672
##
## $nrDisc
## [1] 2
##
## $eigenvalues
## mean sd
## 1.143239 2.058771
##
## $gMean
## mean sd
## 3.223073 2.022943
##
## $hMean
## mean sd
## 2.978389 2.145948
##
## $iqRange
## mean sd
## 1.700000 1.275408
##
## $kurtosis
## mean sd
## -0.8105361 0.7326910
##
## $mad
## mean sd
## 1.0934175 0.5785782
##
## $max
## mean sd
## 5.425000 2.443188
##
## $mean
## mean sd
## 3.464500 1.918485
##
## $median
## mean sd
## 3.612500 1.919364
##
## $min
## mean sd
## 1.850000 1.808314
##
## $nrCorAttr
## [1] 0.5
##
## $nrNorm
## [1] 1
##
## $nrOutliers
## [1] 1
##
## $range
## mean sd
## 3.575 1.650
##
## $sd
## mean sd
## 0.9478671 0.5712994
##
## $sdRatio
## [1] 1.277229
##
## $skewness
## mean sd
## 0.06273198 0.29439896
##
## $sparsity
## mean sd
## 0.08874363 0.13456821
##
## $tMean
## mean sd
## 3.470556 1.904802
##
## $var
## mean sd
## 1.143239 1.332546
##
## $wLambda
## [1] 0.02343863
```

Note that, in the first example the values and the cardinality of the measure are different since the correlation between the attributes were computed using the instances for each class separately. The `post.processing`

methods are applied in these measures since they return multiple values. To define which them should be applied use the `summary`

parameter, as detailed in the `post.processing`

method.

Information theoretical meta-features are particularly appropriate to describe discrete (categorical) attributes, but they also fit continuous ones using a discretization process. These measures are based on information theory. For instance, `normClassEnt`

and `mutInf`

are the normalized entropy of the class and the common information shared between each attribute and the class in the dataset, respectively. To list the measures of this group use `ls.infotheo()`

. The following examples illustrate these measures:

```
## [1] "attrConc" "attrEnt" "classConc" "classEnt" "eqNumAttr" "jointEnt"
## [7] "mutInf" "nsRatio"
```

```
## Extract all information theoretical measures
inf.iris <- infotheo(Species ~ ., iris)
## Extract two information theoretical measures
infotheo(Species ~ ., iris, features=c("normClassEnt", "mutInf"))
```

```
## $mutInf
## mean sd
## 0.8439342 0.4222026
```

The Information theoretical group can use one additional parameter called `transform`

. Using the default value `transform=TRUE`

the continuous attributes will be discretized. The following example shows the use of this definition:

```
## Ignore the discretization process
aux <- cbind(class=iris$Species, iris)
infotheo(Species ~ ., aux, transform=FALSE)
```

```
## $attrConc
## mean sd
## NA NA
##
## $attrEnt
## mean sd
## 1.584963 NA
##
## $classConc
## mean sd
## 1 NA
##
## $classEnt
## [1] 1.584963
##
## $eqNumAttr
## [1] 1
##
## $jointEnt
## mean sd
## 1.584963 NA
##
## $mutInf
## mean sd
## 1.584963 NA
##
## $nsRatio
## [1] 0
```

The information theoretical measures return a list named by the requested measures. The `post.processing`

methods are applied in some measures since they return multiple values. To define which them should be applied use the `summary`

parameter, as detailed in the section **Post Processing Methods**.

These measures describe characteristics of the investigated models. These meta-features can include, for example, the description of the DT induced for a dataset, like its number of leaves (`leaves`

) and the number of nodes (`nodes`

) of the tree. The following examples illustrate these measures:

```
## [1] "leaves" "leavesBranch" "leavesCorrob" "leavesHomo"
## [5] "leavesPerClass" "nodes" "nodesPerAttr" "nodesPerInst"
## [9] "nodesPerLevel" "nodesRepeated" "treeDepth" "treeImbalance"
## [13] "treeShape" "varImportance"
```

```
## Extract all model.based measures
land.iris <- model.based(Species ~ ., iris)
## Extract three model.based measures
model.based(Species ~ ., iris, features=c("leaves", "nodes"))
```

```
## $leaves
## [1] 9
##
## $nodes
## [1] 8
```

The DT model based measures return a list named by the requested measures. The `post.processing`

methods are applied in these measures since they return multiple values. To define which them should be applied use the `summary`

parameter, as detailed in the `post.processing`

method.

Landmarking measures are simple and fast algorithms, from which performance characteristics can be extracted. These measures include the performance of simple and efficient learning algorithms like Naive Bayes (`naiveBayes`

) and 1-Nearest Neighbor (`oneNN`

). The following examples illustrate these measures:

```
## [1] "bestNode" "eliteNN" "linearDiscr" "naiveBayes" "oneNN"
## [6] "randomNode" "worstNode"
```

```
## Extract all landmarking measures
land.iris <- landmarking(Species ~ ., iris)
## Extract two landmarking measures
landmarking(Species ~ ., iris, features=c("naiveBayes", "oneNN"))
```

```
## $naiveBayes
## mean sd
## 0.96000000 0.04661373
##
## $oneNN
## mean sd
## 0.95333333 0.05488484
```

The performance extraction of these measures without a cross validation step can cause model overfitting in the data. Therefore the `landmarking`

function has the parameter `folds`

to define the number of `k`

-fold cross-validation and the parameter `score`

to select the performance measure. The following example show how to set this value:

```
## Extract one landmarking measures with folds=2
landmarking(Species ~ ., iris, features="naiveBayes", folds=2)
```

```
## $naiveBayes
## mean sd
## 0.95333333 0.02828427
```

```
## Extract one landmarking measures with folds=2
landmarking(Species ~ ., iris, features="naiveBayes", score="kappa")
```

```
## $naiveBayes
## mean sd
## 0.93729051 0.07213352
```

The landmarking measures return a list named by the requested measures. The `post.processing`

methods are applied in these measures since they return multiple values. To define which them should be applied use the `summary`

parameter, as detailed in the `post.processing`

method.

The relative group is the landmarking with sampling and ranking strategies. The sampling strategy decreases the computational cost of the landmarking by selecting a subsample of the original examples. The ranking strategy capture relative information between the performance of the algorithms. The following examples illustrate these measures:

```
## [1] "bestNode" "eliteNN" "linearDiscr" "naiveBayes" "oneNN"
## [6] "randomNode" "worstNode"
```

```
## Extract all relative measures
real.iris <- relative(Species ~ ., iris)
## Extract all relative measures with half of the samples
relative(Species ~ ., iris, size=0.5)
```

```
## $bestNode
## mean sd
## bestNode 2 6
##
## $eliteNN
## mean sd
## eliteNN 4.5 3.5
##
## $linearDiscr
## mean sd
## linearDiscr 6 2
##
## $naiveBayes
## mean sd
## naiveBayes 7 1
##
## $oneNN
## mean sd
## oneNN 4.5 3.5
##
## $randomNode
## mean sd
## randomNode 3 5
##
## $worstNode
## mean sd
## worstNode 1 7
```

```
## $naiveBayes
## mean sd
## naiveBayes 2 1
##
## $oneNN
## mean sd
## oneNN 1 2
```

Clustering measures extract information about dataset based on external validation indexes. The main ideia is measure the complexity of the dataset using indexes able to check information about the predictive attributes and the label. The following examples illustrate these measures:

`## [1] "vdu" "vdb" "int" "sil" "pb" "ch" "nre" "sc"`

```
## Extract all clustering measures
clus.iris <- clustering(Species ~ ., iris)
## Extract two clustering measures
clustering(Species ~ ., iris, features=c("vdu", "vdb"))
```

```
## $vdu
## [1] 0.05848053
##
## $vdb
## [1] 0.7513707
```

Several meta-features generate multiple values and `mean`

and `sd`

are the standard method to summary these values. In order to increase the flexibility, the `mfe`

package implemented the post processing methods to deal with multiple measures values. This method is able to deal with descriptive statistic (resulting in a single value) or a distribution (resulting in multiple values).

The post processing methods are setted using the parameter `summary`

. It is possible to compute min, max, mean, median, kurtosis, standard deviation, among others. Any R method, can be used, as illustrated in the following examples:

```
## Apply several statistical measures as post processing
statistical(Species ~ ., iris, "cor",
summary=c("kurtosis", "max", "mean", "median", "min", "sd",
"skewness", "var"))
```

```
## $cor
## kurtosis max mean median min sd
## -1.9476130 0.9628654 0.5941160 0.6231906 0.1175698 0.3375443
## skewness var
## -0.1814291 0.1139362
```

```
## Apply quantile as post processing method
statistical(Species ~ ., iris, "cor", summary="quantile")
```

```
## $cor
## quantile.0% quantile.25% quantile.50% quantile.75% quantile.100%
## 0.1175698 0.3817045 0.6231906 0.8583006 0.9628654
```

```
## $cor
## non.aggregated1 non.aggregated2 non.aggregated3 non.aggregated4
## 0.1175698 0.8717538 0.4284401 0.8179411
## non.aggregated5 non.aggregated6
## 0.3661259 0.9628654
```

Beyond these R default methods, two additional post processing methods are available in the `mfe`

package: `hist`

and `non.aggregated`

. The first computes a histogram of the values and returns the frequencies of in each bins. The extra parameters `bins`

can be used to define the number of values to be returned. The parameters `min`

and `max`

are used to define the range of the data. The second is a way to obtain all values from the measure and has the same effect of the use of an empty list. The following code illustrate examples of the use of these post processing methods:

```
## $cor
## hist.breaks1
## "0"
## hist.breaks2
## "0.2"
## hist.breaks3
## "0.4"
## hist.breaks4
## "0.6"
## hist.breaks5
## "0.8"
## hist.breaks6
## "1"
## hist.counts1
## "1"
## hist.counts2
## "1"
## hist.counts3
## "1"
## hist.counts4
## "0"
## hist.counts5
## "3"
## hist.density1
## "0.833333333333333"
## hist.density2
## "0.833333333333333"
## hist.density3
## "0.833333333333333"
## hist.density4
## "0"
## hist.density5
## "2.5"
## hist.mids1
## "0.1"
## hist.mids2
## "0.3"
## hist.mids3
## "0.5"
## hist.mids4
## "0.7"
## hist.mids5
## "0.9"
## hist.xname
## "c(0.117569784133002, 0.871753775886583, 0.42844010433054, 0.817941126271576, 0.366125932536439, 0.962865431402796)"
## hist.equidist
## "TRUE"
```

```
## Apply histogram as post processing method and customize it
statistical(Species ~ ., iris, "cor", summary="hist", bins=5, min=0, max=1)
```

```
## Warning in plot.window(xlim, ylim, "", ...): "bins" is not a graphical
## parameter
```

```
## Warning in plot.window(xlim, ylim, "", ...): "min" is not a graphical
## parameter
```

```
## Warning in plot.window(xlim, ylim, "", ...): "max" is not a graphical
## parameter
```

```
## Warning in title(main = main, sub = sub, xlab = xlab, ylab = ylab, ...):
## "bins" is not a graphical parameter
```

```
## Warning in title(main = main, sub = sub, xlab = xlab, ylab = ylab, ...):
## "min" is not a graphical parameter
```

```
## Warning in title(main = main, sub = sub, xlab = xlab, ylab = ylab, ...):
## "max" is not a graphical parameter
```

`## Warning in axis(1, ...): "bins" is not a graphical parameter`

`## Warning in axis(1, ...): "min" is not a graphical parameter`

`## Warning in axis(1, ...): "max" is not a graphical parameter`

`## Warning in axis(2, ...): "bins" is not a graphical parameter`

`## Warning in axis(2, ...): "min" is not a graphical parameter`

`## Warning in axis(2, ...): "max" is not a graphical parameter`

```
## $cor
## hist.breaks1
## "0"
## hist.breaks2
## "0.2"
## hist.breaks3
## "0.4"
## hist.breaks4
## "0.6"
## hist.breaks5
## "0.8"
## hist.breaks6
## "1"
## hist.counts1
## "1"
## hist.counts2
## "1"
## hist.counts3
## "1"
## hist.counts4
## "0"
## hist.counts5
## "3"
## hist.density1
## "0.833333333333333"
## hist.density2
## "0.833333333333333"
## hist.density3
## "0.833333333333333"
## hist.density4
## "0"
## hist.density5
## "2.5"
## hist.mids1
## "0.1"
## hist.mids2
## "0.3"
## hist.mids3
## "0.5"
## hist.mids4
## "0.7"
## hist.mids5
## "0.9"
## hist.xname
## "c(0.117569784133002, 0.871753775886583, 0.42844010433054, 0.817941126271576, 0.366125932536439, 0.962865431402796)"
## hist.equidist
## "TRUE"
```

```
## $cor
## non.aggregated1 non.aggregated2 non.aggregated3 non.aggregated4
## 0.1175698 0.8717538 0.4284401 0.8179411
## non.aggregated5 non.aggregated6
## 0.3661259 0.9628654
```

It is also possible define an userâ€™s post processing method, like this:

```
## Compute the absolute difference between the mean and the median
my.method <- function(x, ...) abs(mean(x) - median(x))
## Using the user defined post processing method
statistical(Species ~ ., iris, "cor", summary="my.method")
```

```
## $cor
## my.method
## 0.02907459
```

In this paper the `mfe`

package, aimed to extract meta-features from dataset, has been introduced. The functions supplied by this package allow both their use in MtL experiments as well as perform data analysis using characterization measures able to describe datasets. Currently, six groups of meta-features can be extracted for any classification dataset. These groups and features represent the standard and the state of the art characterization measures.

The `mfe`

package was designed to be easily customized and extensible. The development of the `mfe`

package will continue in the near future by including new meta-features, group of measures supporting regression problems and MtL evaluation measures.